Help with pre-calculus questions?

Question

I have a few questions that have been bothering me, could you show me how to answer them, I don't necessarily want the answer I need to know how you got it.

1. What are three irrational numbers whose sum is a rational number?

2. What are 2 irrational numbers whose product is a rational number?

Thanks for any help you can give me.

Answer 1

1.irrational numbers are numbers such as 1/2,5/3...so 1/3+1/3+1/3=3/3=1....

2.2/3 * 3/2 =1

Answer 2

1. ??

2. square root of 2 and negative square root of two

Answer 3

For 1., One trick is that whenever you add an irrational number to a rational number, the answer is irrational.

So, 5 - sqrt(2) is irrational.  Then you can try different coefficients in front of the sqrt(2) until you find your 3 numbers that fit the answer.

For 2., a square root is irrational, unless it's a perfect square (1,4,9,16,25,etc.)

And, when multiplying square roots, sqrt(a) * sqrt(b) = sqrt(a*b)

So, sqrt(8) * sqrt(2) = sqrt(16)